One of the main importance of modular forms in number theory is that
spaces of modular forms are generated by those with rational Fourier coefficients.
The "period theory" gives another natural rational structure of modular forms.
A striking result by Zagier [1]} states that this rational information of
modular forms
can be written as a single product of Kronecker series \(F_{\tau }(u,v)\)  which is a Jacobi form.
The recent results in [2]}, [3]} show that Eisenstein-Kronecker numbers have a rich arithmetic nature, such as a connection with the special Hecke \(L\) -function over imaginary quadratic fields and Katz' two-variable p-adic Eisenstein measure.
